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      <h1 class="p_Heading1" style="page-break-after: avoid;"><span class="f_Heading1">Model</span></h1>

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<p class="p_Normal">In the literature, different implementations of the MPC principle have been proposed, with different model structures. In the application we are considering, the real-time constraints and the MIMO structure of the model are well described by a linear discrete state space model (sampled version of the continuous process) of the form:</p>
<p class="p_Normal">&nbsp;</p>
<p style="text-indent: 47px; line-height: 1.38; margin: 0px 0px 17px 0px;"><img src="embim5.png" width="261" height="25" style="margin:1px; border:none" alt="" /></p>
<p style="text-indent: 47px; line-height: 1.38; margin: 0px 0px 17px 0px;"><img src="embim6.png" width="181" height="25" style="margin:1px; border:none" alt="" /></p>
<p class="p_Normal">In the current algorithm the process is represented by the the vestibular system. It is located in the inner ear and is composed by the semicircular canals and the otolith organs. The former sense the angular rotation and the latter linear motion. &nbsp;For the semicircular canal, the transfer function that can best relate the sensed angular velocity to the acceleration stimulus in a MC control problem is the following:</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><img src="embim7.png" width="326" height="41" style="margin:1px; border:none" alt="" /> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<span style="font-size: 11pt; font-family: Calibri,Vectora,'Droid Sans','Open Sans',Frutiger,sans-serif; font-style: italic;">(2)</span></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"> The otoliths are described in terms of the transfer function (3) that relates the sensed response to the specific acceleration stimulus:</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><img src="embim8.png" width="340" height="40" style="margin:1px; border:none" alt="" /> &nbsp; &nbsp; &nbsp; &nbsp;<span style="font-size: 11pt; font-family: Calibri,Vectora,'Droid Sans','Open Sans',Frutiger,sans-serif; font-style: italic;">(3)</span></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal" style="text-align: center;"><img alt="mtncng_image6" width="442" height="321" style="margin:0px auto 0px auto;width:442px;height:321px;border:none" src="mtncng_image6.png"/></p>

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